On the left is the result of my render in the viewport. And on the right - in the Chaos Player (without or with default aces correction). Similar results are obtained if I open the file in MPlay.
How can I achieve the same look as in the viewport? What transformation and how I need to apply?

rastarokot
What transformation and how I need to apply?

You covered it up in the screenshot
It's at the bottom right next to ACES dropdown